How to make transparent material in cycles?
An image texture with alpha(transparency) data can be used to make transparent materials. Do note that in order for alpha textures to work the image file format requires an alpha channel or be a grayscale mask.


  UPDATE
  
  Though my original answer is still applicable and functions. There have been many updates and enhancements since then. One of them being the inclusion of a PBR shaders, Principled BSDF hese specifically. Which, as of v2.8, now also has an Alpha input. Simplifying transparency in many ways.


The following examples utilize a 2px by 2px checker pattern with full black and full alpha transparency.
Blender 2.8
Node setup using 'Alpha Channel' with Principled shader:


Master opacity scale is from -1 to +1
Positive values decreases opacity
Negative values increases opacity of masked (transparent) area.

Blender 2.7
In this example; the Transparent Shader is set to white #FFFFFF which produces full transparency. This is then connected to the top input of 2 Mix Shaders.

Alpha from Image Texture is connected to the factor input of first Mix Shader. This takes the alpha data from the image and essentially applies it as a mask.

The color data from the image is not used in this case. Though, when applicable, can be connected to the color input of a shader. Such as mesh based hair and eyelashes for example.

The first Mix Shader connects to the bottom of the second. This allows control of the overall opacity.
Alpha node setup/example:

A black and white and/or grayscale image can be substituted.
Black being fully transparent and white being fully opaque.
Use color output instead of alpha.

Grayscale node setup/example:>Note:


  Some raster formats that support alpha are:
  
  
  OpenEXROpen Source format released by ILM.Designed with CGI workflow in mind.Your image editor may lack support out-of-box.
  JPEG 2000 - Not original JPEGLossy formatSupport may potentially be limited.
  GIFLimited to 256 colorsCan be animated
  PNGIndexed color has faulty alpha handling. Be sure to use RGB/A mode.
  
  
  I would suggest use of OpenEXR when working with raster images containing an alpha channel. For Photoshop users I recommend the exr-io plugin.
  For those using vector images. To my knowledge SVG is the prime candidate.





  Note 2:
  The shader used for color can be changed as desired and/or needed. This will also work with volumetric shaders as well. However do understand that volumetrics work a little differently than surface shaders. Any further detail on that would be getting a little too far off topic.



Special thanks to Mr Zak and troy_S for their insights in the comments.
Happy Blending!